A Unified Framework for Common Fixed Point Results in Suprametric Spaces with Applications to Volterra Integral Equations

OpenAlex · English

This paper develops a systematic common fixed point theory within the framework of suprametric spaces, a recently introduced generalization of metric spaces that accommodates a broader class of distance structures through a nonlinear relaxation of the triangle inequality. We establish several common fixed point theorems for pairs of self-mappings satisfying distinct contractive conditions, specifically Banach-type, Reich-type, Ćirić-type, and rational Gupta–Saxena type contractions, in the setting of complete suprametric spaces. Each theoretical result is accompanied by a concrete example that explicitly verifies the respective contractive hypothesis and confirms the existence and uniqueness of the common fixed point. To demonstrate the practical utility of the developed framework, the main results are applied to establish the existence and uniqueness of solutions to Volterra integral equations of the second kind, modeled via associated integral operators on the space of continuous functions endowed with a suprametric. The suprametric structure, by encompassing classical metric and b-metric spaces as special cases, renders the presented results both comprehensive in scope and broadly applicable to nonlinear problems in analysis and mathematical physics.