Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Theta$- contraction mappings andto prove some best proximity point results for t...

In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method  and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. F...

In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of ...

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

In this work, we first introduce almost contraction mappings for a pair of two in cone metric spaces over Banach algebras (CMSBA). Then, observe that the class such setting contains those many well known mappings. Finally, prove some fixed point theorems, and obtain $(S,T)$-stability results Jungck iterations CMSBA.

recently, zhang and song [q. zhang, y. song, fixed point theory forgeneralized $varphi$-weak contractions,appl. math. lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. in this paper, we prove a common fixed point theorem fora family of compatible maps. in fact, a new generalization of zhangand song's theorem is given.

The current study attempts to identify a new generalized metric space structure, referred as partial modular b−metric, that extends both via b−metric and explains the topological aspects of implementing examples. In addition, contraction mapping modified interpolative almost E−type is determined, which an interpretation bestowed with E−contraction well simulation function fixed point theorem en...

This work is devoted to presenting a new four-step iterative scheme for approximating fixed points under almost contraction mappings and Reich–Suzuki-type nonexpansive (RSTN mappings, short). Additionally, we demonstrate that the proposed algorithm converges faster than variety of other current schemes. Furthermore, scheme’s ?2—stability result established corroborating example given clarify co...