Indian Muslim Freedom Fighters Based in Afghanistan and Soviet Russia

At the outbreak of the First Word War, the Indian Muslim freedom fighters headed towards Afghanistan and thence to Soviet Russia to devise a strategy to pulverize the British Indian government through an alliance of the powers that were hostile to the British Imperialism in India such as Germany, Turkey, Czarist Russia and Soviet Russia. The present paper takes into account the life struggle of a few spirited individuals such as Mawlana Abdur Rahim alias Maulv Bashir, Maulvi Muhammad Ali Quāuri, Mawlana Barakatullah Bhopali, Mawlana Ubayd Allah Sindhi and a host of others who found their way towards Afghanistan with the avowed intention of the liquidation of the British Imperialism from India. The activities of these Freedom fighters apparently did not bring about immediate tangible results in terms of the freedom of India; however, they contributed to the complete freedom of Afghanistan and in subsequent years brought the goal of the freedom of their own country nearer.

Some Generalizations of the Banach Fixed Point Theorem: Single Valued and Multi-Valued Mappings

In [N. Mizoguchi, W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177–188] the authors gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy certain contractive conditions. In this paper, we establish some results for multi-valued mappings that satisfy a generalized contractive condition in a way that it contains Mizoguchi’s result as one of its special cases. In addition, our results not only improve the results of Kiran and Kamran [Q. Kiran, T. Kamran, Nadler’s type principle with high order of convergence, Nonlinear Anal. TMA 69 (2008) 4106–4120] and some results of Agarwal et al. [R.P. Agarwal, Jewgeni Dshalalow, Donal O’Regan, Fixed point and homotopy results for generalized contractive maps of Reich type, Appl. Anal. 82 (4) (2003) 329–350] but also provide the high order of convergence of the iterative scheme and error bounds. As an application of our results, we obtain an existence result for a class of integral inclusions.