A NEW ITERATIVE APPROACH FOR ESTIMATING FIXED POINTS UNDER CHATTERJEE SUZUKI CONDITION

Abstract

Fixed point (FP) theory is an important subject of analysis that can give effective techniques for handling nonlinear issues. The existence and uniqueness of solutions tointegral and differential equations are proven using FP theory. Computing the exact valueof a solution to a nonlinear issue is frequently challenging. In such a case, the proposed solution's approximate value is always considered. Finding a FP using particular schematic methods requires analyzing various features of FPs, such as data dependence, convergence, and stability. Research on new iterative techniques for functional equation solving and FP analysis is active and has many useful applications. The furst iterative approach for ap-proximating a FP of a contraction mapping T on a nonempty subset S of a Banach space(BN-space) D is the Picard iterative approach. Numerous authors have created a varietyof methods for estimating the FP. This paper proposes an efficient new iterative approachfor approximating the FP under the Chatterjee-Suzuki-C CSC condition which is called the R* iterative approach. In the beginning, a new iterative approach is provided. Afterward,it is shown via analytical demonstration that the suggested method converges to an FP for contraction map more quickly than some well-known methods. Furthermore, some important weak and strong convergence results of the proposed iterative approach are establishedin the setting of BN-space. To support the primary conclusions, a brief example has been presented to demonstrate the eciency of the recommended iterated procedure via the class of the dened mappings that fulfill CSC condition.