Necessary and Sufficient Optimality Conditions in Nonlinear Programming Involving B-locally Connected Function

B-locally connected function is defined. Nonlinear programming problem is considered involving this function. Kuhn-Tucker type sufficient optimally conditions are given under the hypotheses that the right differential with respect to an arc at an optimal point exists. Also Fritz –John type necessary optimality criteria under the hypothesis that the right differentials, at an optimal point, of the objective and the active constraint functions are arc wise connected and inactive constraint functions are continuous.