Existence results of certain nonlinear polynomial and integral equations via ϝ-contractive operators

Abstract

In this manuscript, the concept of $ \digamma $-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of $ G $-metric space, which is termed Jaggi-Suzuki-type hybrid $ \digamma $-($ G $-$ \alpha $-$ \phi $)-contraction, and invariant point results which cannot be inferred from their cognate ones in metric space are established. The results obtained herein provide a new direction and are generalizations of several well-known results in fixed point theory. An illustrative, comparative example is constructed to give credence to the results obtained. Furthermore, sufficient conditions for the existence and uniqueness of solutions of certain nonlinear polynomial and integral equations are established. For the purpose of future research, an open problem is highlighted regarding discretized population balance model whose solution may be investigated from the techniques proposed herein.

Keywords

• $ \digamma $-contraction
• $ g $-metric
• fixed point
• admissible mappings
• nonlinear integral equation