The main aim of this article is to achieve a new iterative scheme to gain the unique common positive definite solution to a pair of non-linear matrix equations. We do this by using the notion of enriched contractions. First, we come by a couple of common fixed point results involving the newly introduced enriched contractions in pair concepts. Then we obtain a couple of results indicating sufficient conditions for existence of unique common positive definite solution and an iterative scheme to get such solution to two different pair of matrix equations. Further, we authenticate these two results by suitable examples.
We establish some fixed point results for multivalued mappings under the Hardy-Rogers type contraction in the setting of b-metric spaces. Some of those results extend and generalize many known theorems either in metric and b-metric spaces to the b-metric spaces or for the self mappings to multivalued mappings. We also significantly improve results obtained by Chifu, C. and Petru & cedil;sel, G. (2017). We also establish the Ulam-Hyres stability using retraction-displacement technique notably avoiding the proximinality condition. Additionally, we address the open question posed by Petrusel, A. Petrusel, G. and Yao, J. C. (2020). providing an affirmative answer even in the b-metric spaces. For the first time, we also establish a Bogin-type fixed point theorem for multivalued mappings. Several examples are provided to exemplify the improvement of our results with respect to the classical one, as well as an application to a generalized class of coupled fixed-point problems.
This paper presents an adaptive algorithm for solving enriched contraction variational inequality problems, using the set of fixed points of an enriched nonexpansive mapping as a constrained set. The algorithm is defined within the framework of unique geodesic spaces. In each iteration, the scheme uses only two embedded geodesic segments and does not require the computation of any metric projection. The method requires one evaluation of an enriched nonexpansive mapping T-1 and an enriched contraction T-2 at every iteration. The convergence analysis of the proposed scheme is performed in the setting of CAT(0) spaces, and a numerical example is provided to support the findings.
In this paper, we present a b-metric approach to dq-K-metric spaces and its application to the stability of functional equations.
In this paper we shall study, in terms of a metric and an order relation, the existence, uniqueness and data dependence for the solutions of integral equation x(t) = (g(1)(t) + integral(t)(a) K-1(t, s, x(s))ds) . (g(2)(t) + integral(t)(a) K-2(t, s, x(s))ds), t is an element of [a, b]. Our results extend the results from I.M.Olaru An Integral Equation via Weakly Picard Operators, Fixed Point Theory, 11(2010), No. 1, pp 97-106.
