Point Theorems For Non-self Mappings Research Articles

Fixed Point Theorems for Non-self Mappings Using Disconnected Graphs

Objectives: To prove the fixed point theorems for non-self mappings using disconnected graphs. Method: Graph theoretical approach is adopted to prove the fixed point theorems for non-self mappings. In all the previous works, connected graphs were used for establishing the results, but it is demonstrated in this work that disconnected graphs are best suited, and this new approach simplifies the proofs to a greater extent. Findings: The fixed point theorems by Banach, Kannan, Chatterjea, and Bianchini are proved using the new methodology. Novelty: An important part of the results concerning fixed point theorems is proving the iterated sequence to be a Cauchy sequence, and this is amalgamated with the edge sequence of the disconnected graph. Subject Classification: 54H25, 47H10 Keywords: Non-self mapping, Iterated sequence, Disconnected graph, Edge sequence, Fixed point

Fixed point theorems for non-self mappings on strictly star-shaped sets in generalized Banach spaces

Fixed point theorems for non-self mappings on strictly star-shaped sets in generalized Banach spaces

PAIR OF NON-SELF-MAPPINGS AND COMMON FIXED POINTS IN PARTIAL METRIC SPACES

Gajić and Rakočević proved a common fixed point theorem for non-self mappings on a Takahashi convex metric space. In this paper, we prove a common fixed point theorem on a pair of non-self mappings obeying specified conditions on a convex partial metric space. We also provide an illustrative example on the use of the theorem.

A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces

Abstract In this paper we prove existence and uniqueness of a common fixed point for non-self coincidentally commuting mappings with nonlinear, generalized contractive condition defined on strictly convex Menger PM-spaces proved.

Fixed Point Theorems For Non-Self Mappings With Nonlinear Contractive Condition In Strictly Convex Menger $$PM\mbox{-}$$Spaces

We prove existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition defined in strictly convex Menger $$PM\mbox{-}$$ spaces.

Fixed point theorems for self and non-self F-contractions in metric spaces endowed with a graph

The main results obtained in this paper are fixed point theorems for self and non-self GF-contractions on metric spaces endowed with a graph. Our new results are generalization of recently fixed point theorems for self mappings on metric spaces and also fixed point theorems for non-self mappings in Banach spaces by using the concept of new type of contractive mappings namely F-contractions.

Fixed point Theorems for Non-self mappings with nonlinear contractive condition in strictly convex FCM-spaces

In this paper we define convex, strict convex and normal structures for sets in fuzzy cone metric spaces. Also, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition will be proved, using the notion of strictly convex structure. Moreover, we give some examples illustrate our results.

Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces

In this paper, we introduce a class of nonlinear contractive mappings in metric space. We also establish common fixed point theorems for these pair of non-self mappings satisfying the new contractive conditions in the convex metric space . An example is given to validate our results. The results generalize and extend some results in literature.

Some fixed point theorems for non-self mappings of contractive type with applications to endpoint theory

In this paper, in the setting of complete metric spaces we establish some fixed point theorems for non-self mappings of contractive type satisfying either the Reich–Zaslavski property or the approximate fixed point property. As applications, we obtain some results in endpoint theory.

Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces

Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces

Common best proximity points in complex valued b-metric spaces

In this paper, we obtain some results on common best proximity points for non-self mappings between two subsets of complex valued b-metric spaces. For this purpose, first we generalize some well-known results that were proved in classic metric spaces on complex valued b-metric space by some new definitions. Second we present a type of contractive condition and develop a common best proximity point theorem for non-self mappings in complex-valued b-metric spaces. Our results are supported by some examples.

An extension of Assad-Kirk’s fixed point theorem for multivalued nonself mappings

In the present paper, taking into account the recent developments on the theory of fixed point, we give some fixed point results for multivalued nonself mappings on complete metrically convex metric spaces. Our main result properly includes the famous Assad-Kirk fixed point theorem for nonself mappings. Also, we provide a nontrivial example which shows the motivation for such investigations of multivalued nonself contraction mappings.

On Contraction Mappings and Fixed Point Theorems in 2-Normed Spaces

In this paper, we introduce j contraction mappings in 2-normed spaces and we show that the mappings have a unique fixed point in 2-Banach spaces. Also, we introduced a new fixed point theorem for nonselfmappings applying the definition of retraction to 2-Banach spaces.

New Existence Results for Fixed Point Problem and Minimization Problem in Compact Metric Spaces

We first present some new existence theorems for fixed point problem and minimization problem in compact metric spaces without assuming that mappings possess convexity property. Some applications of our results to new fixed point theorems for nonself mappings in the setting of strictly convex normed linear spaces and usual metric spaces are also given.

Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dynamic programming

In this paper, we prove some common fixed point theorems for two pairs of non-self weakly compatible mappings enjoying common limit range property, besides satisfying a generalized φ-weak contractive condition in symmetric spaces. We furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature. We extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings. Finally, we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming.

An integral type fixed point theorem for multi-valued mappings employing strongly tangential property

Sintunavarat and Kumam (W. Sintunavarat, P. Kumam, Gregus-type common fixed point theorems for tangential multi-valued mappings of integral type in metric spaces, Int. J. Math. Math. Sci. 2011 12 (Article ID 923458)) extended the tangential property to hybrid pair of mappings which generalizes the idea of tangential property due to Pathak and Shahzad (H.K. Pathak, N. Shahzad, Gregus type fixed point results for tangential mappings satisfying contractive conditions of integral type, Bull. Belg. Math. Soc. Simon Stevin 16(2) (2009) 277–288). In the present paper, we introduce the notion of strong tangential property and utilize the same to prove an integral type metrical common fixed point theorem for non-self mappings. An illustrative example is also furnished to support our main result. Our results are corrected, improved and generalized versions of a multitude of relevant common fixed point theorems of the existing literature.

Fixed point theorems for nonlinear non-self mappings in Hilbert spaces and applications

Abstract Recently, Kawasaki and Takahashi (J. Nonlinear Convex Anal. 14:71-87, 2013) defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings (Kocourek et al. in Taiwan. J. Math. 14:2497-2511, 2010) and strict pseudo-contractive mappings (Browder and Petryshyn in J. Math. Anal. Appl. 20:197-228, 1967). They proved fixed point theorems for such mappings. In this paper, we prove fixed point theorems for widely more generalized hybrid non-self mappings in a Hilbert space by using the idea of Hojo et al. (Fixed Point Theory 12:113-126, 2011) and Kawasaki and Takahashi fixed point theorems (J. Nonlinear Convex Anal. 14:71-87, 2013). Using these fixed point theorems for non-self mappings, we proved the Browder and Petryshyn fixed point theorem (J. Math. Anal. Appl. 20:197-228, 1967) for strict pseudo-contractive non-self mappings and the Kocourek et al. fixed point theorem (Taiwan. J. Math. 14:2497-2511, 2010) for super hybrid non-self mappings. In particular, we solve a fixed point problem. MSC:Primary 47H10; secondary 47H05.

Non-self mappings in modular spaces and common fixed point theorems

Abstract The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.

Common Fixed Point Theorem for Non-Self Mappings Satisfying Generalized Ćirić Type Contraction Condition in Cone Metric Space

We prove common fixed point theorem for coincidentally commuting nonself mappings satisfying generalized contraction condition of Ciric type in cone metric space. Our results generalize and extend all the recent results related to non-self mappings in the setting of cone metric space.

A Mönch type fixed point theorem under the interior condition

In this paper we show that the well-known Mönch fixed point theorem for non-self mappings remains valid if we replace the Leray–Schauder boundary condition by the interior condition. As a consequence, we obtain a partial generalization of Petryshyn's result for nonexpansive mappings.