رشتے برائے فروخت
آئو …آئو…خدا کے بندو!
عیش کے فرزندو
میں تمھیں آج ایک چیز دکھائوں
ایک انوکھی ،تمھارے مطلب کی چیز
جس سے تمھیں سکون ملتا ہے
اور لبوں پہ طنزیہ مسکراہٹیں سجتی ہیں
یہ لیجیے……!
مفاد پرستی کی محبت
حسدکی آگ میں جلتے رشتے
ایذا کے کیچڑ میں لتھڑے رشتے
آنسو بہاتے اور سسکتے رشتے
پتھر کی طرح سخت ،مگر کانچ سے نازک رشتے
بانسری کی طرح کھو کھلے ،عداوت کے سُر نکالتے رشتے
پیاروں کے خون میں رنگے رشتے
جن کا کوئی نعم البدل نہیں
خلوص کا زہر اگلتے رشتے
ایسا زہر جس کا کوئی تریاک نہیں
سب …لے جائو
اور بدلے میں چند مسکراہٹیں دے جائو
جو ان رشتوں کے باعث چھن گئی ہیں
چند خوشیاں دے دو
جو ادھوری خواہشوں کی مانند چبھ رہی ہیں
Ijmāʿ is an important mode of Ijtihād and well known principle of Islamic Sharʿiah. Historically it is evident that incidence of Ijmāʿ )Consensus( restricted only to four Caliphates of Islam only. This Collective Ijtihād and Collective Opinion was actually the decision of the Islamic State followed and obeyed by the all Muslims specially by "Ṣaḥābah" (Companions of the Holy Prophet), this is why it is called Ijmāʿ-e- Ṣaḥābah. These decisions were applicable and binding to all Muslims living elsewhere in the world, because at that time there was centralized ruling system (Khilāfat-e-Wāḥidah). Now Muslim world has split into many states, so every state has its own decision making institutions and hence such Ijtihād and Ijmāʿ, Islamic Legislation Activities should be validated within those states as Ijtihād and Ijmāʿ except issues relevant to general interest as whole human being and all Muslims. In such issues International level consensus of Islamic Jurists would be required. "Ijmāʿ", actually it is the same processes. More over any "Ijmāʿ" held in a time period can be revoked by any new situation in future as per requirement of the time. It is the inevitable demand of dynamism of Islam to correlate it to every need of the time.
The thesis is devoted to the weighted criteria for integral operators with positive ker- nels in variable exponent Lebesgue and amalgam spaces. Similar results for multiple kernel operators defined with respect to a Borel measure in the classical Lebesgue spaces are also obtained. More precisely, we established necessary and sufficient conditions on a weight function v governing the boundedness/compactness of the weighted positive kernel operator Kv f (x) = v(x) x 0 k(x, y)f (y)dy from Lp(·) (R+ ) to Lq(·) (R+ ) under the local log-H ̈lder continuity condition and the decay condition at o infinity on the exponents p and q. In the case when Kv is bounded but not compact, two-sided estimates of the measure of non-compactness (essential norm) for Kv are obtained in terms of the weight v and kernel k. Criteria guaranteeing the boundedness /compactness of weighted kernel operators defined on R+ (resp. on R) in variable ex- ponent amalgam spaces are found. The kernel operators under consideration involve, x for example, the Riemann-Liouville transform Rα f (x) = 0 f (t) dt, (x−t)1−α 0 < α < 1. Necessary and sufficient conditions ensuring weighted estimates for maximal and po- tential operators in variable exponent amalgam spaces are also established under the local log-H ̈lder continuity condition on exponent of spaces. Further, we establish o criteria on measures governing the boundedness of integral operators with product positive kernels defined with respect to a Borel measure in the classical Lebesgue spaces. Finally, we point out that Fefferman-Stein type inequality for the multi- ple Riemann-Liouville transform defined with respect to a product Borel measure is derived.