COINCIDENCE AND FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTION MAPPING ON b-METRIC SPACES

Weak condition for generalized multi-valued [formula omitted]-weak contraction mappings

In this paper we prove some results on the existence of coincidence points for weak hybrid contractions on symmetric spaces. These results improve and generalize some known results. In particular, recent fixed point results due to Hicks [3] are generalized. 2000 Mathematics Subject Classification. 47H10, 54H25

ObjectivesWe explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized ({check{psi }}, hat{eta })-weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings.ResultIn partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

In this paper, we introduce a new concept of generalized cyclic (κh, ϕL)S-weak contraction mappings and establish some coincidence point results for such mappings in complete partially ordered Menger PM-spaces. Our results generalize the main results of Nashine (Nonlinear Anal. 75:6160-6169, 2012) and Gopal et al. (Appl. Math. Comput. 233:955-967, 2014). We also obtain the corresponding coincidence point theorems for generalized cyclic (κh, ϕL)S-weak contractions in partially ordered metric spaces. MSC: 47H10; 54H25

The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized (v,o)-weak contractions in partially ordered cone metric spaces. Also, some illustrative examples are presented.

Motivated by the ideas of F -weak contractions and F , R g -contractions, the notion of F w , R g -contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for F w , R g -contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.

The purpose of this paper is to prove some results on fixed point, coincidence point, coupled coincidence point and coupled common fixed point for the mappings satisfying generalized \((\phi, \psi)\)-contraction conditions in complete partially ordered \(b\)-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. A few examples are illustrated to support our findings.

In this manuscript, we establish a coincidence point and a unique common fixed point theorem for (psi ,varphi )-weak cyclic compatible contractions. We also present a fixed point theorem for a class of Λ-weak cyclic compatible contractions via altering distance functions. Our results extend and improve some well-known results in the literature. We provide examples to analyze and illustrate our main results.

Coincidence point results via generalized (ψ,ϕ)-weak contractions in partial ordered b-metric spaces with application

We introduce ordered quasicontractions and g-quasicontractions in partially ordered metric spaces and prove the respective coincidence point and (common) fixed point results. An example shows that the new concepts are distinct from the existing ones. We also prove fixed point theorems for mappings satisfying so-called weak contractive conditions in the setting of partially ordered metric space. Hence, generalizations of several known results are obtained. Mathematics Subject Classification (2010): 47H10; 47N10.

In 2009 Qingnian Zhang and Yisheng Song proved fixed point theory for two φ–weak contraction functions. We generalize this result by finding fixed point and coincidence point for three single-valued φ–weak contraction T1, T2, T3 defined on a complete metric space.

ObjectivesIn this paper we present some fixed point theorems for self mappings satisfying generalized (phi , psi )-weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results.ResultWe obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized (phi , psi )-weak contraction mappings in partially ordered complete b-metric space.

In this paper coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of Harjani et al. (2011). Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partially ordered complete metric spaces are deduced.

In this work, in the setting of a vector-valued metric space X, the fixed point inclusion x∈G(x),x∈X governed by a multi-valued operator G:X⊸X satisfying a weak contraction type condition on its graph is studied. Some stability results are obtained and the coincidence point problem involving two multi-valued operators is also studied. The best proximity point problem in vector-valued metric spaces is finally discussed.

Coincidence and fixed point theorems for generalized [formula omitted]-weak nonlinear contraction in ordered [formula omitted]-metric spaces