نامی کوئی بغیر مشقت نہیں ہوا
نحمدہ ونصلی علی رسولہ الکریم امّا بعد فاعوذ بااللہ من الشیطن الرجیم
بسم اللہ الرحمن الرحیم
معزز اسا تذہ کرام اور میرے ہم مکتب شاہینو!
آج مجھے جس موضوع پر اظہار خیال کرنا ہے وہ ہے:’’نامی کوئی بغیر مشقت نہیں ہوا‘‘
صدرِذی وقار!
اس عالم رنگ و بو میں جہاں کہیں بھی انسان موجود ہے اس کے دل میں یہ خواہش بڑی شدومد کے ساتھ انگڑائیاں لے رہی ہے کہ وہ معروف ہو جائے، اس کی عظمت کے ڈنکے بجنے لگیں ، اس کی چار دانگ عالم میں مشہوری ہو جائے ، اس کے سر پر ناموری کا تاج سج جائے۔
جنابِ صدر!
شہرت کا عقاب بلند پروازی کرسکتا ہے ، مجدی و سروری کی آرزو پوری کی جاسکتی ہے، نامی کہنے کا خواب پورا ہوسکتا ہے، عزت و عظمت کی فاختہ اپنے گھر کی منڈیر پر بٹھائی جاسکتی ہے، گلستان و چمنستان میں بڑے پن کے گلہائے رنگا رنگ کھلائے جاسکتے ہیں، اپنے اعزاء واقارب، احباب واصدقاء کے درمیان اپنی بڑائی کا لوہا منوایا جا سکتا ہے ،لیکن
جنابِ صدر!
اس کے لیے تساہل وغفلت کی عبا کو تار تار کرنا ہوگا ، اس کے لیے جہد مسلسل اور پیہم کدوکاوش کرنی ہوگی ، اس کے لیے تیشٔہ فرہاد استعمال کرتے ہوئے جوئے شیر لانا ہوگی، اس کے لئے آرام و آسائش کی قربانی دینی ہوگی ، اس کے لیے زندگی کے حسین لمحات کو خیر باد کہنا ہو گا۔
صدرِذی وقار!
تاریخ کے اوراق کی ورق گردانی سے یہ بات مترشحّ ہوتی ہے کہ جن نابغہ ٔروزگار ہستیوں نے مقام ِرفیعہ پر قدم رکھا اللہ تعالیٰ کے فضل و کرم کے ساتھ ساتھ ان کی محنت بھی شامل تھی ، ان کی شبانہ روز کوششوں اور کاوشوں کا بڑا عمل دخل تھا، ان کی محنتِ...
BackgroundMany women enjoy wearing high heels despite knowing they can harm their feet. Many uncomfortable conditions can originate from wearing this shoe, leading to biomechanical changes in ankle joints. Hence, the study is aimed to identify the effects of massage therapy in improving muscular flexibility among women wearing high heels. MethodologyForty female participants with chronic heel pain were included in the single-blinded, randomized controlled trial. Participants were divided into Group-A (Stretching and deep heat) and Group-B (petrissage and deep heat). The treatment was performed for 4 weeks, 3 sessions/week in both groups. Foot function index and ankle dorsiflexion were recorded at baseline and after 4-weeks of intervention. ResultsForty female participants with a mean age of 28.23±6.24 were recruited. Both groups showed significant improvement in all three variables, i.e. Pain, disability, and ankle dorsiflexion. However, Group-B showed more significant results with mean differences of 1.80±2.22 and 4.1±6.7 (p<0.05) for pain and disability, respectively. A similar result was observed for ankle dorsiflexion in which a mean difference of 0.95±1.08 in the left and 1.25±1.12 in the right ankle was observed. ConclusionBoth treatment programs are highly effective in reducing pain, reducing disability, and improving ankle joint ROM. However, petrissage massage and deep heating were superior to superficial heat with static stretching for females with chronic heel pain. DOI: https: //doi. Org/10.59564/amrj/01.01/006
The aim of this research is to investigate some contractions and establish the existence results of single and multivalued mappings in frame work of some abstract space. Banach (1922) presented a fixed point theorem, namely Banach contraction theorem, which states that, a contraction mapping has a unique fixed point in a complete metric space. This theorem is widely applicable in proving the existence of solutions of functional equations under certain conditions. This theorem is based upon the iterative process, so it can be easily implemented on computer. This theorem was a revolution in fixed point theory. Later on , several generalizations of this theorem have been obtained. Fixed point results are widely studied in the framework of topological, metric and ordered oriented spaces. It is interesting to study that a nonlinear functional equation T(x) = x (where T is some linear or nonlinear operator defined on metric or fuzzy metric space) has either a solution or possess no solution. If the nonlinear functional equation has any solution, then it is interesting to find some algorithms which lead to an appropriate solution, but if nonlinear functional equation has no solution, then to try and find some approximate solution. The approximation, optimization and fixed point theory incorporate the main theme of nonlinear analysis. The best approximation theory is applicable in variety of problems arising in nonlinear functional analysis. Banach (1922) fixed point theorem is vastly applicable in proving the existence of solutions of functional equations under certain conditions. Many authors generalized Banach contraction principle in various directions. To address the question, if a nonlinear functional equation has no solution, it is recommended to approximate the solution which solves the optimization problem such that d(x, T x) is minimum. Ky Fan’s (Fan (1969)) best approximation result has been used when some nonlinear functional equations have no solution. In this thesis, best proximity point results in non-Archimedean fuzzy metric space are proved and some optimal best proximity point results are also obtained. These results provides the existence of optimal approximate solutions to some equations which have no solution. Further, fuzzy optimal coincidence point results for different proximal contractions in the framework of complete non-Archimedean fuzzy metric space are obtained. These results also holds in fuzzy metric spaces when some mild assumptions are added in the domain of involved mappings. In the next part of thesis, best proximity point results in a complete non-Archimedean fuzzy metric space with ordered structure have been discussed. Further, a class of multivalued mappings is introduced which satisfies Suzuki type generalized contractive condition in the framework of fuzzy metric spaces and some fixed point results are obtained for such kind of mappings. In next part of this thesis, Suzuki type contraction conditions are further generalized as Suzuki type F−contraction fuzzy mapping in ordered metric spaces. As an application, a common fixed point result for hybrid pair of single and multivalued mappings, the existence and uniqueness of common bounded solution of functional equations arising in dynamic programming are obtained. The obtained results generalize and extend various results in the existing literature. In each chapter, some examples are provided, which shows the validity of the results along with couple of remarks about the comparison of obtained results with the existing ones in the literature.