New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

The purpose of this paper is to introduce a new iterative algorithm to approximate the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Also, we show that our proposed iterative algorithm converges weakly and strongly to the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Furthermore, it is proved analytically that our new iterative algorithm converges faster than one of the leading iterative algorithms in the literature for almost contraction mappings. Some numerical examples are also provided and used to show that our new iterative algorithm has better rate of convergence than all of S, Picard-S, Thakur and M iterative algorithms for almost contraction mappings and generalized α-nonexpansive mappings. Again, we show that the proposed iterative algorithm is stable with respect to T and data dependent for almost contraction mappings. Some applications of our main results and new iterative algorithm are considered. The results in this article are improvements, generalizations and extensions of several relevant results existing in the literature.

Fixed Point of Almost Contraction in b -Metric Spaces

In this paper, we introduce a generalized multivalued ( α , L)-almost contraction in the b -metric space. Furthermore, we prove the existence and uniqueness of the fixed point for a specific mapping. The result presented in this paper extends some of the earlier results in the existing literature. Moreover, some examples are given to illuminate the usability of the obtained results.

Fixed points of Suzuki-type generalized multivalued (f,θ,L)- almost contractions with applications

In this paper, we define Suzuki type generalized multivalued almost contraction mappings and prove some related fixed point results. As an application, some coincidence and common fixed point results are obtained. The results proved herein extend the recent results on fixed points of Kikkawa Suzuki type and almost contraction mappings in the frame work of complete metric spaces. We provide examples to show that obtained results are proper generalization of comparable results in the existing literature. Some applications in homotopy, dynamic programming, integral equations and data dependence problems are also presented.

A new perspective for multivalued weakly Picard operators

This research contains some recent developments about multivalued weakly Picard operators on complete metric spaces. In addition, taking into account both multivalued ?-contraction and almost contraction on complete metric spaces, we present a new perspective for multivalued weakly Picard operators. Finally, we give a nontrivial example showing that the investigation of this paper is significant.

Fixed point theorems for Presic almost contraction mappings in orbitally complete metric spaces endowed with directed graphs

The main aim of this paper is to introduce a class of generalized contractions in product spaces in the sense of Presiˇ c. Some examples and fixed point theorems for such introduced mappings in the setting of orbitally ´ complete metric spaces are proved. The results presented here extend and include many existing several results in the literature.

Multivalued almost contractions in metric space endowed with a graph

The main goal of this paper is to introduce a multivalued almost contraction on a metric space with a graph. In terms of this new contraction, we establish some fixed point results on graph.

Fixed point theorems for cyclic non-self single-valued almost contractions

Let X be a Banach space, A and B two non-empty closed subsets of X and let T : A ∪ B → X be an operator. We define the notion of cyclic non-self almost contraction and we give a corresponding fixed point theorem.

Existence and Uniqueness of Best Proximity Points for Generalized Almost Contractions

The purpose of this paper is to elicit some interesting extensions of generalized almost contraction mappings to the case of non-self-mappings withα-proximal admissible and prove best proximity point theorems for this classes. Moreover, we also give some examples and applications to support our main results.