Asian Journal of Mathematics and Computer Research

This paper establishes a common fixed point theorem for two multivalued mappings in a complete cone bmetric- like space. The setting is a real Banach space ordered by a cone, and the mappings are assumed to take nonempty, closed and bounded values. A rational-type integral contraction condition is formulated through a continuous, non-decreasing control function that vanishes only at the zero element of the cone. Under these hypotheses, an alternating iterative sequence is constructed from the two mappings. The contractive inequality is then applied to show that the successive distances converge to the zero element and that the generated sequence is Cauchy. By completeness of the cone b-metric-like space, the sequence converges to a point in the underlying set. The closedness of the image sets ensures that the limit belongs to the images of both mappings, and hence it is a common fixed point. Several corollaries are derived by reducing the result to a single multivalued mapping, to a linear choice of the control function, and to standard contraction-type conditions. An example on the interval [0, 1], with values in a cone of non-negative continuously differentiable functions, is provided to illustrate the assumptions and applicability of the theorem. The results extend fixed point statements for multivalued mappings while retaining the self-distance feature of cone b-metric-like spaces.