رسم عثمانی میں غیر موجود اور صحیح سند سے ثابت قراءات کا حکم

Some of the variant readings of the Holy Quran having a sound chain of narration are not included in the Uthmanic Maṣāḥif (Codices). Hence, following three probabilities can be deduced about these readings; First: Those were abrogated in ʿArḍah Akhīrah (the last revision). Second: Those might be among those explanatory notes of the Holy Text by Prophet Muhammad (SWA) that were erroneously written by a few companions within the actual text of Quran considering them a part of the Quran. Third: Those may belong to such Aḥruf (readings) that were authentically transmitted from the Messenger of Allah (SWA) but, they were not mentioned in the orthography of the Uthmanic Maṣāḥif by the compilers due to any possible reason. To us, if we come across any authentically narrated recitation of the senior Qurrāʾ companions that seems contrary to the orthography of the Uthmanic Maṣāḥif and there is no proof of their being from the second category, then, it is better to consider them from the third category instead of the first one.

Generalized Fuzzy Coincidence and Fixed Point Theorems

Generalized Fuzzy Coincidence and Fixed Point Theorems In this thesis, the notion of intuitionistic fuzzy b-metric spaces (shortly, IFbMS) has been introduced. Fixed point theorems of contractive mappings in IFbMS are formulated and proved to generalize the well-known Banach, Kannan and Chatterjea type results. Zamfirescu type result is also created in fuzzy b-metric space. Coincidence points and common fixed point of weakly compatible mappings in IFbMS along with the stimulating examples are obtained as well. Further, the existence of common fixed point of a family of multivalued maps in closed ball in complete intuitionistic fuzzy metric space is obtained and some valuable consequences are attained from this result. Moreover, a common coincidence point theorem for a pair of L-fuzzy mappings and a non-fuzzy mapping under a generalized ?-contraction condition in a metric space in association with the Hausdorff distance is proved and enhanced with a practical example. A generalized common coincidence point theorem with the?? ∞ metric on 1- cuts of L-fuzzy sets is achieved as well and it is concluded that under the alike circumstances there may be a coincidence point of a pair of multivalued mappings and a point to point mapping. A few corollaries are assembled to generalize many important results with the?? ∞ metric on L-fuzzy sets. Some applications of the obtained results are presented as well. Further, the existence theorems regarding fixed points and common fixed points of intuitionistic fuzzy set-valued maps for Meir-Keeler type contraction in complete metric spaces are established and proved. In addition, some common fuzzy fixed points of fuzzy set-valued mappings having ?-contraction in a complete metric space are obtained by using an integral type contraction condition. In this approach, numerous valuable current and previous results have been generalized. To indicate the strength of the main result, an interesting example is furnished.