Best proximity points for asymptotic proximal pointwise weaker Meir–Keeler-type ψ-contraction mappings

AbstractIn this paper, we study the new class of an asymptotic proximal pointwise weaker Meir–Keeler-type ψ-contraction and prove the existence of solutions for the minimization problem in a uniformly convex Banach space. Also, we give some an example for support our main result

Generalized Proximal ψ

We generalized the notion of proximal contractions of the first and the second kinds and established the best proximity point theorems for these classes. Our results improve and extend recent result of Sadiq Basha (2011) and some authors

Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces

We give some initial properties of a subset of modular metric spaces and introduce some fixed-point theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied

Optimal Approximate Solution for (α,β )γ-Contraction Mappings in Metric Spaces with Applications

In this paper, we extend the concept of generalized proximal contractions of the first kind to proximal (a,b )y -contractions types A and B. We show with examples that our new classes of mappings is real generalization of many known classes of non-self and self mappings in literature. We also introduce some condition for proving the best proximity point theorems in such classes. Applying our new concepts, we obtain best proximity point results on metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph

Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions

The purpose of this article is to resolve a global optimization problem for quasi-noncyclic relatively nonexpansive mappings by giving an algorithm that determines an optimal approximate solution of the following minimization problem, min x ∈ A d ( x , T x ) , min y ∈ B d ( y , T y ) and min ( x , y ) ∈ A × B d ( x , y ) ; also, we provide some illustrative examples to support our results. As an application, the existence of a solution of the analytic complex function is discussed

Fixed Point and Common Fixed Point Theorems for Generalized Weak Contraction Mappings of Integral Type in Modular Spaces

We prove new fixed point and common fixed point theorems for generalized weak contractive mappings of integral type in modular spaces. Our results extend and generalize the results of A. Razani and R. Moradi (2009) and M. Beygmohammadi and A. Razani (2010)

Some Geometric Properties of Lacunary Sequence Spaces Related to Fixed Point Property

The main purpose of this paper is considering the lacunary sequence spaces defined by Karakaya (2007), by proving the property (β) and Uniform Opial property