Orbital b-Metric Spaces and Related Fixed Point Results on Advanced Nashine-Wardowski-Feng-Liu Type Contractions with Applications

Abstract

In this article we prove some novel fixed-point results for a pair of multivalued dominated mappings obeying a new generalized Nashine-Wardowski-Feng-Liu- type contraction for orbitally lower semi-continuous functions in complete orbital b-metric space. Furthermore, some new fixed-point theorems for dominated multivalued mappings are established in the scenario of ordered complete orbital b-metric space. Some examples are offered to demonstrate the validity of our new results' premise. To demonstrate the applicability of our findings, applications for a system of nonlinear Volterra type integral equations and fractional differential equations are shown. These results extend the theoretical results of Nashine et al. (Nonlinear Anal. Model. Control. 26(3)(2021), 522–533).2010 Mathematics Subject Classification: 47H04; 47H10; 54H25