We introduce some generalizations of Prešić type contractions and establish some fixed point theorems for mappings satisfying Prešić-Hardy-Rogers type contractive conditions in metric spaces. Our results generalize and extend several known results in metric spaces. Some examples are included which illustrate the cases when new results can be applied while old ones cannot.

We establish the existence and uniqueness of solutions for a class of nonlinear Volterra integral and integro-differential equations using fixed-point theorems for a new variant of cyclic (ϕ, ψ, θ )-contractive mappings. Nontrivial examples are given to support the usability of our results. MSC: 47H10; 54H25