A STUDY ON SOME PROBLEMS ON EXISTENCE OF SOLUTIONS FOR NONLINEAR FUNCTIONAL-INTEGRAL EQUATIONS

In this paper, we prove the existence of solutions of some nonlinear functional- integral equation by using a fixed point theorem which satisfy the Darbo condition. The results extend the corresponding results of many authors. In the sequel, we give an example of our main result to highlight the realized improvements.

BRUCK FORMULA FOR A PERTURBED LIPSCHITZIAN ITERATION OF LIPSCHITZ PSEUDOCONTRACTIVE MAPS

The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution （ fixed point） of pseudocontractive operators and its variants. The object is to introduce a perturbed iteration method for proving the convergence of sequence of Lipschitzian pseudocontractive mapping using approximate fixed point technique. This iteration can be ued for nonlinear operators which are more general than Lipschitzian pseudocontractive operator and Bruck iteration fails for proving their convergence. Our results generalize the results of Chidume and Zegeye.

Trade Credit Policy Between Supplier-Manufacturer-Retailer for Ameliorating/Deteriorating Items

This paper is related to the advancement of the inventory models for ameliorating items and focused on the real-life business situation as with the time the deterioration rate of ameliorating items is increased.In the global world,every supply chain entities as suppliers/manufacturers/retailers want to increase the consumption of their goods without any losses.For this,he/she tries to lure manufacturer/retailers by offering some discounts,i.e.credit period for settling the account.The problem states that the manufacturer purchases the ameliorating items from the supplier,where the supplier offers his/her credit period to settle the account.The manufacturer purchases ameliorating items(like pigs,fishes,ducklings,etc.)and take those items as rawmaterial;when the livestock matures the manufacturer sells it to the retailer and offer credit time for settling the account.Reason to propose the model is when the quantities of livestock become larger,then the manufacturer faces difficulty in maintaining all the livestock.In such a situation,the traditional method(without offering credit period)fails to provide the maximum profit to the manufacturer.Therefore,in order to get maximum profit,the manufacturer needs some more realistic scientific outlook for making decisions.The proposed model provides a more realistic assumption of business markets,by offering credit policy.In the introduced model,manufacturer faces amelioration and deterioration rate simultaneously due to the growth and the death of livestock.The amelioration and deterioration rates are assumed as theWeibull distribution type.Shortages allowed only for the retailer,which is partially backlogged.The main goal of this paper is to minimize the total relevant inventory cost for both the manufacturer and the retailers,by finding the optimal replenishment policy.Themathematical formulation with optimal solutions for manufacturer and retailers are given.Convexity and existence of the proposed model via numerical examples and graphical representations are explained.Finally,the conclusions with some future research direction are discussed.