Asia Mathematika, Vol 10, issue 1, pages: 12--16.

Study on Fixed Point Result for Special Mappings

K. Prudhvi
Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, Telangana, India.

Received: 17 Feb 2026 | Accepted: 04 May 2026 | Final Version: 30 May 2026

Abstract

In this paper, study on existence of fixed point result for mappings defined on CCM (Complete Cone Metric)-Spaces $(X,\rho)$ satisfying a G-Contractive condition defended on another function.

Keywords:
Contractive condition, fixed point, sequentially convergent, sub sequentially convergent.

1. Introduction

Banach contraction principle is the first and foremost important result in fixed point theory it was appeared in Banach’s [6] thesis in 1922. The Banach contraction principle in 1968 Kannan [12] analyzed a substantially new type of contraction condition. Later on many authors were inspired with these results, extended and generalized in different ways(see for e.g.[ 1-5, 7-11, 13-21]). Huang and Zhang [9] introduced the cone metric space, where the set of real numbers is replaced by an ordered Banach space. They obtained some fixed point results in cone metric space. Later on many authors were inspired by these results; they have been extending these results in different dimensions ( see for e.g. [1-8, 8-11,13-22]). In recent developments in this area for non explosive map in cone metric spaces (see for e.g. [1-6]. Recently Beiravand, Moradi, et. al. [7] obtained two fixed point theorems for special mappings. In this paper we proved a fixed point result for special mappings.

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