The paper aims at initiating and exploring the concept of extended metric known as the Strong Altering JS-metric, a stronger version of the Altering JS-metric. The interrelation of Strong Altering JS-metric with the b-metric and dislocated metric has been analyzed and some examples have been provided. Certain theorems on fixed points for expansive self-mappings in the setting of complete Strong Altering JS-metric space have also been discussed.

         In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved  fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.

   In this paper we prove a theorem about the existence and uniqueness common fixed point for two uncommenting self-mappings which defined on orbitally complete G-metric space. Where we use a general contraction condition.
 

      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

    In this paper, we prove some coincidence and common fixed point theorems for a pair of discontinuous weakly compatible self mappings satisfying generalized contractive condition in the setting of Cone-b- metric space under assumption that the Cone which is used is nonnormal. Our results are generalizations of some recent results.

In the context of normed space, Banach's fixed point theorem for mapping is studied in this paper. This idea is generalized in Banach's classical fixed-point theory. Fixed point theory explains many situations where maps provide great answers through an amazing combination of mathematical analysis. Picard- Lendell's theorem, Picard's theorem, implicit function theorem, and other results are created by other mathematicians later using this fixed-point theorem. We have come up with ideas that Banach's theorem can be used to easily deduce many well-known fixed-point theorems. Extending the Banach contraction principle to include metric space with modular spaces has been included in some recent research, the aim of study proves some pro

       In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

   This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.