Rogers Type Research Articles

Ϝ-Contraction of Hardy–Rogers type in supermetric spaces with applications

This article focuses on studying some fixed-point results via Ϝ-contraction of Hardy–Rogers type in the context of supermetric space and ordered supermetric space. We also introduced rational-type z-contraction on supermetric space. For authenticity, some illustrative examples and applications have been included.

Fredholm integral equation in composed-cone metric spaces

AbstractThe current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples of a type I and type II composed cone metric space, which is not a cone metric space, are given. We establish some results of fixed point precisely about Hardy–Rogers type contraction on C2CMS and provide examples. Finally, we present an application of our results and how our results solve the Fredholm integral equation of generalizing several existing and unique fixed point theorems.

Double composed metric-like spaces via some fixed point theorems

<p>The manuscript introduces the concept of a double-composed metric-like space, which is an extension of the notion of a double-composed metric space. In this new space, the self-distance is not necessarily zero, but if the distance metric equals zero, it must be for identical points of distance. Furthermore, this paper presents several results related to this novel concept in the literature, with a particular focus on Hardy–Rogers type contractions. It establishes fixed point theorems accompanied by some illustrative examples that elucidate the findings. Finally, this research provides an application to nonlinear integral equation to substantiate our theorems.</p>

Inhomogeneous Diophantine approximation for generic homogeneous functions

This paper is a sequel to [Monatsh. Math. 194 (2021) 523–554] in which results of that paper are generalized so that they hold in the setting of inhomogeneous Diophantine approximation. Given any integers [Formula: see text] and [Formula: see text], any [Formula: see text], and any homogeneous function [Formula: see text] that satisfies a certain nonsingularity assumption, we obtain a biconditional criterion on the approximating function [Formula: see text] for a generic element [Formula: see text] in the [Formula: see text]-orbit of [Formula: see text] to be (respectively, not to be) [Formula: see text]-approximable at [Formula: see text]: that is, for there to exist infinitely many (respectively, only finitely many) [Formula: see text] such that [Formula: see text] for each [Formula: see text]. In this setting, we also obtain a sufficient condition for uniform approximation. We also consider some examples of [Formula: see text] that do not satisfy our nonsingularity assumptions and prove similar results for these examples. Moreover, one can replace [Formula: see text] above by any closed subgroup of [Formula: see text] that satisfies certain integrability axioms (being of Siegel and Rogers type) introduced by the authors in the aforementioned previous paper.

Several q-series transformation formulas and new Hecke–Rogers type series identities

Several q-series transformation formulas and new Hecke–Rogers type series identities

Fixed point theorems in complex valued b-metric spaces

In this paper, we have proved common fixed point theorems using Hardy and Rogers type contraction condition in complex-valued b-metric spaces The results of the paper extend the results proved in S. Ali [1].

Functional response of the predatory mite, Typhlodromus bagdasarjani (Acari: Phytoseiidae) to protonymphs of Eotetranychus frosti (Acari: Tetranychidae) on four apple cultivars

The functional response of natural enemies and their interactions may be affected by host plant characters. Functional response of the adult females of the predatory mite, Typhlodromus bagdasarjani Wainstein and Arutunjan to protonymphs of Eotetranychus frosti (McGregor) on four apple cultivars Imperial Gala, Kohanz Golab, Granny Smith and Lebanon Red was investigated. The protonymphs of E. frosti were offered to the adult female of the predator at densities of 2, 4, 8, 16, 32, 64 and 128 on apple leaf discs (4 cm<sup>2</sup>). The number and length of trichomes on the lower surface of each apple cultivar were measured. The highest and lowest number of trichomes were observed in Granny Smith and Kohanz Golab, respectively. Typhlodromus bagdasarjani adult females exhibited the type II functional response on E. frosti protonymphs regardless of apple cultivars. Also, the values of attack rate (a) and handling time (T<sub>h</sub>) were determined using the Rogers's type II model. Adult females of T. bagdasarjani had the highest attack rate (a) (0.0747 h<sup>1</sup>) and the shortest handling time (0.7005 h) on Kohanz Golab, and the lowest attack rate (0.0334 h<sup>1</sup>) and the longest handling time (1.1189 h) was on Granny Smith. The theoretical maximum predation rate (T/T<sub>h</sub>) on Kohanz Golab, Imperial Gala, Lebanon Red and Granny Smith were 34.26, 33.79, 26.85 and 21.45 prey/day, respectively. The estimated value of a/T<sub>h</sub> indicated that T. bagdasarjani was most effective against E. frosti on Kohanz Golab with lowest number of trichomes. The finding of this study shows that the predation and searching activity of the predator was affected by trichome density and length of the apple leaves.

Coupled Fixed Points for Hardy–Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

In this paper we generalize Hardy–Rogers maps in the context of coupled fixed points. We comment on the symmetry of some of the coefficients involved in the Hardy–Rogers condition, and thus, we deduce a simpler formula. We generalize, with the help of the obtained main theorem, some known results about existence and uniqueness of market equilibrium in duopoly markets. As a consequence, we ascertain that the equilibrium production should be equal for both market participants provided that they have symmetric response functions. With the help of the main theorem, we investigate and enrich some recent results regarding market equilibrium in duopoly markets. We define a generalized response function that includes production and surpluses. Finally, we illustrate a possible application of the main result in the investigation of market equilibrium when the payoff functions are non-differentiable.

Generalized q-Difference Equations for q-Hypergeometric Polynomials with Double q-Binomial Coefficients

In this paper, we apply a general family of basic (or q-) polynomials with double q-binomial coefficients as well as some homogeneous q-operators in order to construct several q-difference equations involving seven variables. We derive the Rogers type and the extended Rogers type formulas as well as the Srivastava-Agarwal-type bilinear generating functions for the general q-polynomials, which generalize the generating functions for the Cigler polynomials. We also derive a class of mixed generating functions by means of the aforementioned q-difference equations. The various results, which we have derived in this paper, are new and sufficiently general in character. Moreover, the generating functions presented here are potentially applicable not only in the study of the general q-polynomials, which they have generated, but indeed also in finding solutions of the associated q-difference equations. Finally, we remark that it will be a rather trivial and inconsequential exercise to produce the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional forced-in parameter p is obviously redundant.

Hecke–Rogers type series representations for infinite products

Hecke–Rogers type series representations for infinite products

On Fixed Point Result in Double Controlled Metric Spaces

In this paper, we introduce Hardy and Rogers type contractions in the class of double controlled metric spaces and establish fixed point theorem. Our result are generalization of some known results of literature. We also provide example to illustrate significance of the established result .

Truncated Hecke–Rogers type series—part II

Truncated Hecke–Rogers type series—part II

Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction

In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of g -interpolative Hardy–Rogers type contractions in b -metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.

Some fixed point results for multi-valued mappings in metric-like and quasi metric-like spaces

We establish the existence of fixed point for F-contractive multivalued mappings of Hardy–Rogers type in metric-like spaces. Then, we introduce a new notion called bilateral approximate fixed points for multivalued mappings and establish a common bilateral approximate fixed point result for two [Formula: see text]-dominated multivalued contractive mappings in the sense of [M. Arshad, Z. Kadelburgb, S. Radenovic, A. Shoaibe and S. Shukla, Filomat. 31(11) (2017) 3041–3056] on a closed ball of a K-sequentially complete quasi metric-like space. Finally, one can observe that the common bilateral approximate fixed point results coincide with common fixed point results, whenever we reduce the quasi metric-like spaces to metric-like spaces.

New fixed point results for F-contractions of Hardy–Rogers type in b-metric spaces with applications

The purpose of this paper is to introduce the notions of extended F-contraction of Hardy–Rogers type, extended F-contraction of Suzuki–Hardy–Rogers type and generalized F-weak contraction of Hardy–Rogers type and to establish some new fixed point results for such kind of mappings in the setting of complete b-metric spaces. These fixed point results improve (and/or) extend those obtained in Vetro (Nonlinear Anal Model Control 21(4):531–546, 2016) and Lukacs and Kajanto (Fixed Point Theory 19(1):321–334, 2018) since some conditions made therein are removed or weakened. In addition, some illustrative examples are provided to show the usability of the obtained results. As an application of our results, we obtain the existence and uniqueness of solutions for certain functional, integral and differential equations.

Interpolative Reich–Rus–Ćirić and Hardy–Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results

The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich–Rus–Ćirić type contraction and Hardy–Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.

Generating functions for some families of the generalized Al-Salam\u2013Carlitz q-polynomials

In this paper, by making use of the familiar q-difference operators D_{q} and D_{q^{-1}}, we first introduce two homogeneous q-difference operators mathbb{T}(mathbf{a},mathbf{b},cD_{q}) and mathbb{E}(mathbf{a},mathbf{b}, cD_{q^{-1}}), which turn out to be suitable for dealing with the families of the generalized Al-Salam–Carlitz q-polynomials phi_{n}^{(mathbf{a},mathbf{b})}(x,y|q) and psi_{n}^{(mathbf{a},mathbf{b})}(x,y|q). We then apply each of these two homogeneous q-difference operators in order to derive generating functions, Rogers type formulas, the extended Rogers type formulas, and the Srivastava–Agarwal type linear as well as bilinear generating functions involving each of these families of the generalized Al-Salam–Carlitz q-polynomials. We also show how the various results presented here are related to those in many earlier works on the topics which we study in this paper.

Fixed Point Problems on Generalized Metric Spaces in Perov’s Sense

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov’s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy–Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam–Hyers stability of the fixed point problem. An example is also given to sustain the presented results.

On Some New Multivalued Results in the Metric Spaces of Perov’s Type

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov’s sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam–Hyers stability are also studied.

Hardy–Rogers Type Iterated Function Systems

In this paper we introduce the concept of Hardy–Rogers type iterated function system and we prove that the fractal operator associated to such a system is a Picard operator. Some examples are provided.